answer all parts of all questions with explanation

. The customer service center for an airline's frequent ier program receives telephone calls from customers in three tiers of their 'equent ier program. Tier 1 customers call according to a Poisson process having a rate of 1.2 per minute. Tier 2 customers call according to a Poisson process having a rate of 2.3 per minute. Tier 3 customers call according to a Poisson [recess having a rate of 4.1 per minute. The three Poisson processes are independent. (a) What is the probability that a total of 12 calls are received during a 90-mond interval? (b) Given that a total of 20 calls are received during a certain time interval. what is the probability that 7 of th were from tier 2 customers? (c) What is the expected value of the number of tier 3 calls received during a 20- minute interval, given that 47 tier 2 calls were received during that same interval? ((1) Given that 4 tier 1 customers called during a 2-minute interval, what is the expected value of the total number of calls dining a 6-minute interval that completely contains that 2minute interval